Trying to solve a boundary value problem

The answer key says that there's no solution to the first part, but there is a solution to the 2nd part. I'm really lost and am not sure how to go about this. I'd greatly appreciate everyone's help on this!!!

y = A cos 2x + B sin 2x.....that would be the complementary solution. How would I go about finding a particular integral? I was gonna do an integrating factor but I think that's only for first-order ODE.

y = A cos 2x + B sin 2x.....that would be the complementary solution. How would I go about finding a particular integral? I was gonna do an integrating factor but I think that's only for first-order ODE.

If the Right side is cosax,sinax, sinax+cosax, then your particular integral is Asinax+Bcosax.

To find A and B, you need to substitute back this into the differential equation and then compare coefficients.